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# Physics and Mirrors Help

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By McGraw-Hill Professional
Updated on Sep 12, 2011

## The Convex Mirror

A convex mirror reflects light rays in such a way that the effect is similar to that of a concave lens. Incident rays, when parallel, are spread out (Fig. 19-8a ) after they are reflected from the surface. Converging incident rays, if the angle of convergence is just right, are collimated by a convex mirror (see Fig. 19-8b ). When you look at the reflection of a scene in a convex mirror, the objects all appear reduced. The field of vision is enlarged, a fact that is used to advantage in some automotive rear-view mirrors.

Fig. 19-8 . (a) A convex mirror spreads parallel incident light rays. (b) The same mirror collimates converging incident light rays.

The extent to which a convex mirror spreads light rays depends on the radius of curvature. The smaller the radius of curvature, the greater is the extent to which parallel incident rays diverge after reflection.

## The Concave Mirror

A concave mirror reflects light rays in a manner similar to the way a convex lens refracts them. When incident rays are parallel to each other and to the axis of the mirror, they are reflected so that they converge at a focal point (Fig. 19-9a ). When a point source of light is placed at the focal point, the concave mirror reflects the rays so that they emerge parallel (see Fig. 19-9b ).

Fig. 19-9 . (a) A concave mirror focuses parallel light rays to a point. (b) The same mirror collimates light from a point source at the focus.

The properties of a concave mirror depend on the size of the reflecting surface, as well as on the radius of curvature. The larger the light-gathering area, the greater is the light-gathering power. The smaller the radius of curvature, the shorter is the focal length. If you look at your reflection in a convex mirror, you will see the same effect that you would observe if you placed a convex lens up against a flat mirror.

Concave mirrors can have spherical surfaces, but the finest mirrors have surfaces that follow the contour of an idealized three-dimensional figure called a paraboloid . A paraboloid results from the rotation of a parabola , such as that having the equation y = x 2 in rectangular coordinates, around its axis. When the radius of curvature is large compared with the size of the reflecting surface, the difference between a spherical mirror and a paraboloidal mirror (more commonly called a parabolic mirror ) is not noticeable to the casual observer. However, it makes a big difference when the mirror is used in a telescope.

## Physics and Mirrors Practice Problem

#### Problem

Suppose that a simple convex lens is made from the same material as a prism that casts a rainbow when white light is shone through it. How does the focal length of this lens for red light compare with its focal length for blue light?

#### Solution

The glass has a higher refractive index for blue light than for red light. Therefore, the glass bends blue light more, resulting in a shorter focal length for blue than for red.

Practice problems of these concepts can be found at: Optics Practice Test

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